How to Compute LBO Returns to Each Party in Equity Rollover?

Scenario here is assuming existing sponsor and management roll over a portion of their equity and a new sponsor comes into the mix. In this case, how does one compute returns? Let's say existing sponsor rolls over $1,000M, mgmt rolls over $500, and new sponsor puts up $1,000M. This means that existing sponsor and new sponsor each own 40% respectively and mgmt owns 20% correct? 

At exit, should the roll-over be considered as the initial invested capital from the existing sponsor and mgmt? Separately, if the existing sponsor and mgmt. earn proceeds from the LBO transaction, should that be factored into cash inflow or excluded? Getting a bit lost as if cash proceeds from initial deal are included, then there would be no cash outflow whatsoever...